Solution de l'Hypoth\`ese de Riemann

In 1859, Riemann had announced the following conjecture : the nontrivial roots (zeros) $s=\alpha +i\beta$ of the zeta function, defined by: $$\zeta (s)={\displaystyle \sum _{n=1}^{+\mathrm{\infty }}\frac{1}{n^s},for\mathrm{\Re }(s)>1}$$ have real part $\alpha ={\displaystyle \frac{1}{2}}$. We give a proof that $\alpha ={\displaystyle \frac{1}{2}}$ using an equivalent statement of Riemann Hypothesis.